Stanley Kubrick was a sucker for order, so he might have appreciated the desire to catalogue his career. However, since the acclaimed director's films often warn against placing too much faith in systems, perhaps he knew that this way madness lies.

Frankly, most of Kubrick's films have fair claim to being number one, so establishing first amongst equals means there were some hard choices along the way – just try not to trigger the doomsday device or start swinging the axe if you don't agree.

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Let's open the pod bay doors and enter an enigmatic, exceptional body of work...

13. Fear and Desire (1953)

Even a genius has to start somewhere. Already a successful magazine photographer and documentary maker, 24-year-old Kubrick directed his debut about a military mission on limited funds – it was shot silently with sound added later.

It was plagued by difficulties, and Kubrick later called it "a completely inept oddity, boring and pretentious". He's half-right: the acting is variable and the over-earnest narration laughable, yet at a lean 61 minutes it's a fascinating primer into themes Kubrick would develop throughout his career. In particular, an uncomfortable set-piece about the treatment of a female prisoner foreshadows Kubrick's fearless ability to provoke audiences.

12. Killer's Kiss (1955)

If you honour Kubrick's wish to disown Fear and Desire, then Killer's Kiss becomes his debut proper, and while it's an obvious leap forward, it's still dwarfed by the brilliance to follow. The narrative – in which a down-and-out boxer's romance with his neighbour is threatened by her sadistic nightclub boss – is strictly B-movie, but Kubrick uses it to perfect his style.

More clearly than any later film, the inky Weegee-inspired visuals display the director's roots in photography, while the location filming on the streets of New York offers the last chance to see the director working in his birthplace before his travels began.

11. Lolita (1962)

"How did they ever make a movie of Lolita?" the posters teased. The answer: "Because Kubrick wanted to." Granted the critical prestige and commercial clout to choose his own projects, he fought Hollywood censorship to bring Vladimir Nabokov's scandalous satirical novel about a paedophile to the screen.

In a decision that would define his subsequent career, Kubrick insisted on shooting this very American road movie entirely in England, a flaw that the film never quite overcomes. Nonetheless, it's a squirm-inducing comedy of cringe, with a never-better James Mason locating the pathos in "pathetic" as he battles not only his own poisonous feelings but also a shrill, monstrous Shelley Winters and sleazy Peter Sellers.

10. Spartacus (1960)

It's apt that a film best known for its cry of solidarity – "I'm Spartacus!" – should be attached to Kubrick's least typical film, made within the Hollywood system at the behest of star/producer Kirk Douglas. Inevitably, Kubrick would later disown Spartacus as hackwork, but it remains proof that he could handle a big budget and deliver a hit movie without dumbing down.

Full of characteristically unsentimental, limb-lopping action and genuinely thoughtful in its cynical study of power and politics, it also marks the first real hint of a comedian in Kubrick, thanks to Peter Ustinov (who, as scene-stealing slave dealer Batiatus, is the only actor to win an Oscar in a Kubrick film).

9. A Clockwork Orange (1971)

It is impossible to separate A Clockwork Orange from the furore that erupted upon its release and Kubrick's subsequent decision to withdraw the film from circulation, at least in Britain. The notoriety has made this a transgressive classic, but it has to be said the unavailability certainly helped its reputation.

The positives? The ultraviolence remains disturbing, its themes are still pertinent and Malcolm McDowell is a pioneer of punk in attitude and fashion. Yet, arguably, this represents the moment Kubrick believed the hype, the reclusive rock-star director who suddenly had to follow 2001 with another "hit album" (and, indeed, during the record store scene you can actually see a copy of the 2001 soundtrack).

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As such, the film is very calculated in its shock value and sermonising; you might say its neatly circular narrative runs like clockwork. It speaks volumes that the film's definitive image (McDowell, eyes agape at the terrors he's forced to watch but unable to look away) came to pass. While McDowell was nearly blinded for art, the rest of us had the option to close our eyes until Kubrick made the switch from anarchist to authoritarian by withdrawing the film and removing our free will.

8. Eyes Wide Shut (1999)

It's the most difficult film to place in the Kubrick canon, given its initially hostile reception and its status as the great director's posthumous swansong. Impossibly hyped at the time as an art-porn film starring Hollywood's golden couple, Tom Cruise and Nicole Kidman, there was an inevitable groan of anticlimax at its frosty, remote lack of titillation.

Nowadays, though, the film's slow-burning Tantric qualities are beginning to assert themselves. Hypnotically slow, strange and sometimes (deliberately) silly, it is unmistakably Kubrickian, but this old master offers as satirical a vision as the same year's youthful Fight Club.

This is a society where financial and sexual avarice are conflated – a Christmas tree in every home, a prostitute on every corner – and wealth numbs feelings. The dreamlike artifice forces us to question the reality of everything (audiences mostly failed to notice that Kubrick swapped some of the nude, masked models between shots, for example); in the cruellest of meta-masterstrokes, that includes Tom 'n' Nic's marriage.

7. Full Metal Jacket (1987)

By 1987, everybody had done their Vietnam movie – and Stanley Kubrick had covered warfare from WW1 to the Napoleonic Wars. So Full Metal Jacket is different; a radical work structurally and aesthetically, which emphasises the madness of military training over the chaos of combat.

Boot camp thus becomes the crucible where men are transformed into killing machines via the brutal monotony of routine. Centred around the blistering energy of R Lee Ermey (a real-life drill sergeant who came to improvise some of cinema's greatest insults – "I bet you're the kind of guy that would f**k a person in the ass and not even have the goddamn common courtesy to give him a reach-around!") it's a bleak comedy, not least in the self-parody of Kubrick as perfectionist.

The second half, although full of iconic moments ("me so horny"), is less essential, but achieves a loopy grandeur in presenting a "Vietnam" that is actually London's Docklands dressed up with napalm and palm trees. It's claustrophobic and chilly, precise and pretentious, but riddled with mad brilliance.

6. The Killing (1956)

In his third film, Kubrick established himself as a vital new voice in cinema – and given how epic his running times would become, The Killing's leanness remains startling. This tale of a daring racetrack robbery is noir stripped to the bone: a terse, tense heist picture defined by the fatalism of its looping chronology, forever repeating the action until the characters become trapped in the grooves.

Inspired by Welles and in turn inspiring Tarantino, the showboating established Kubrick as a talented tyro, capable of executing bravura tracking shots and marshalling a superb cast of character actors. Kubrick cleverly hired hard-boiled author Jim Thompson to write the dialogue, and the writer's brittle, unflinching machine-gun rattle portrays a world where everybody is on the take and kindness is a weakness.

5. Paths of Glory (1957)

War was a subject that Stanley Kubrick returned to again and again, but Paths of Glory remains his finest film on the subject. With its minute focus on one botched WWI assault (and its terrible aftermath), it lays bare a piercing insight into how warfare brings out the worst in mankind, not only in the hellish, barbaric conditions of the trenches but also in how the conditions were engineered by callous generals for whom glory is just a buzzword for career advancement.

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The film's plot is so merciless and meticulous that it has pertinent things to say about any institution; it could be remade as a thriller about the corporate world. It's perhaps Kubrick's definitive statement about how systems tend towards psychopathy; where later, more "perfect" films hid behind irony or elaborate art direction, this is a young man's film, incandescent with rage at the world it depicts. Even the trademark bravura camerawork – the extraordinary tracking shots along the trenches or across no man's land – has a fierce purpose.

It ends with one of the few moments of emotion in Kubrick, as the bloodlust of the soldiers is momentarily silenced by the delicate singing of a German prisoner. If it wasn't obvious enough from the scene that Kubrick had let his guard down, consider that the actress he hired – Christiane Harlan, billed as Susanne Christiansen – would soon become Mrs Kubrick.

4. Dr Strangelove or: How I Learned To Stop Worrying And Love The Bomb (1964)

A great director looks at the world with fresh eyes. There's no better example than the moment Stanley Kubrick took Red Alert, Peter George's ultra-serious novel of nuclear armageddon, and wondered: what if this was funny? The result is a lesson in not being shy about thinking the unthinkable. With merciless logic, Kubrick exposes the flaws in a system designed to be fool-proof. After all, it is the nature of a fool to find a way and Kubrick knew that automated processes don't remove human error; they just hide it better.

Much of it might be a documentary, until you concentrate on the details: a general justifying the world's end because of paranoid delusions about precious bodily fluids; or the delectable double-speak of satirist Terry Southern's dialogue: "Gentlemen, you can't fight in here – this is the War Room!"

The only real giveaway is Peter Sellers's tour-de-force triple performance as British buffoon, American President and the titular Germanic genius, which tips events into the farce promised by the film's ace subtitle. Look closely – the character names; those suggestive shots of mid-air refuelling – and it's obvious this is a film about sex. After all, what else are men to do but use their big weapons to overcompensate for sexual dysfunction? No wonder the film culminates in the ultimate climax.

3. Barry Lyndon (1975)

The unknown sights of the universe? The most ultraviolent impulses of mankind? Easy for a master like Kubrick. Filming something to look like it was shot in the past? Now there's a challenge. Barry Lyndon represents the most extreme example of Kubrick's immaculate technique, with its ravishing imagery inspired by the paintings of old masters.

Insistent that conventional cameras would make his stately locations seem artificial, Kubrick asked NASA to develop specialist lenses so that he could shoot by candlelight.

If the camera was built to travel to the moon, Kubrick's film likewise treats the past as an alien world. Barry Lyndon has none of the cosy familiarity of the period dramas you see on Sunday night telly; it is a cruel, bitterly ironic world in which the people are at the mercy of war, greed and jealousy. The satirical story, from Thackeray's novels, offers a greatest hits of Kubrick's themes as Barry (Ryan O'Neal) journeys through 18th-century society, with its stinging sideswipes at romantic courtship, military madness, the snobbery of class and the hubris that can drive a man to destroy himself.

Too glacial for some tastes, it is often overlooked amidst the more popular films Kubrick made before or since, written off as an exercise in style over substance; indeed, all four of its Oscars (the most of any Kubrick film) were in technical categories. Yet, over three hypnotic hours, it cuts surprisingly deep.

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What starts as a very funny picaresque (driven by a rogue's gallery of British character actors) turns into something moving and tragic, as Barry discovers the limits of his journey from peasant to nobleman.

2. The Shining (1980)

One of Kubrick's enduring strengths is his ability to warp a genre to his own ends. His adaptation of Stephen King's horror novel is a case in point. Kubrick booked a night in a haunted hotel and left audiences so spooked that baffled first-time viewers nominated it for two Razzies (including Kubrick as director).

As a scare story, Kubrick's formidable technique creates a mood of unease from the off, from the labyrinthine production design – lent extra eeriness by pioneering use of the then-novel Steadicam – to the relentless assault of freakish, inexplicable images: blood-filled lifts; cadaverous hotel guests; those creepy twins.

Yet the real genius behind The Shining is that it isn't just a scare story – which is perhaps why King hated it. Never offering a clear-cut explanation, the ambiguity allows plenty of room for manoeuvre: just look at Room 237, the documentary based entirely on mad fan theories. That enables Kubrick to suggest that the madness might lie beyond the supernatural, existing instead in the fractured psyche of failed writer Jack Torrance (Jack Nicholson on towering, silly/sinister form).

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The Shining rewards particular attention as a bleak comedy about marital dysfunction (the centrepiece of a cynical trilogy bookended by Lolita and Eyes Wide Shut) and, given Nicholson's uncanny resemble to the director, as a sly self-portrait of a perfectionist artist driven mad by constant interruption.

How could it be anything else for the number one slot? Kubrick's sci-fi opus is the monolith under whose shadow modern cinema cannot escape. It is the touchstone for the FX-heavy spectacle of space-opera blockbusters but also the intellectual rigour of serious arthouse dramas. And for the director himself, it marked the perfection of his style and proof that an unwavering commitment to experimentation need not put off the paying public.

Subverting expectations from the start (a space movie marooned with the apes at the dawn of time) and refusing easy answers (which bit of the movie is set in 2001, anyway?), Kubrick offers approximately one hour of plot; the rest is pure cinema. Whether spanning centuries in a single, audacious cut or taking us beyond the infinite with avant-garde photographic techniques, the film fuses technique, theme and narrative together in ways that audiences instinctively get yet might which not be fully unpacked over a lifetime.

What is even more obvious today is the ironic contrast between Kubrick's awe-inspiring fusion of sound and image with the characters' complete indifference to their surroundings. At a time when everybody wondered what the future would be like, Kubrick suggested it would be just like the present: banal and routine. A job's a job even if it comes with unrivalled views of the cosmos.

And so Kubrick asks the biggest question: there are lessons to be learnt, but are we capable of learning them? This is a baleful vision of our tendency to exist in thrall life's black monoliths – whether that refers to signposts towards an extra-terrestrial intelligence or to the machines to which we have ceded control. After all, what does NASA do when confronted with proof we're not alone in the universe? They take a photo of it. [Kubrick couldn't possibly have realised this, but the appearance of his totem is a dead ringer for the iPhone, which shows how right he was.]

In other words, 49 years since its release and 18 since its maker passed away, this is one puzzle that still invites solving – playful, preposterous and pioneering. Whatever you think of the film's WTF ending, this was never about the destination but the journey, as indeed was Kubrick's whole career: an attempt to reshape cinema at every turn.